Many modern tablet computers, notebook computers, smart phones, and similar electronic devices include one or more acoustic transducers. For example, a given one of these electronic devices may include a microphone configured to receive sound from a user and a speaker configured to transmit sound to the user. These acoustic transducers are typically positioned inside a solid enclosure that protects the acoustic transducers and other delicate electronic components of the device from the environment. Sound, however, tends to diminish in intensity and fidelity when forced to travel through a solid material. To address this problem, an electronic device may include an acoustic port configured to facilitate sound transmission between air outside the electronic device and an acoustic transducer inside the electronic device. In a particular example, an internal acoustic transducer carried by a dedicated flexible circuit board is positioned near an acoustic port in a covering substrate. The flexible circuit board extends between internal processing circuitry of the electronic device and the area near the acoustic port. A ring of foam or an annular boot is disposed between the acoustic transducer and the covering substrate to seal an acoustic path extending to the acoustic transducer via the acoustic port.